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This paper aims to investigate the approach combine the deep learning (DL) and finite element method for the magneto-thermal coupled problem.

To achieve the DL of electrical device with the hypothesis of a small dataset, with ground truth data obtained from the FEM analysis, U-net, a highly efficient convolutional neural network (CNN) is used to extract hidden features and trained in a supervised manner to predict the magneto-thermal coupled analysis results for different topologies. Using part of the FEM results as training samples, the DL model obtained from effective off-line training can be used to predict the distribution of the magnetic field and temperature field of other cases.

The possibility and feasibility of the proposed approach are investigated by discussing the influence of various network parameters, in particular, the four most important factors are training sample size, learning rate, batch size and optimization algorithm respectively. It is shown that DL based on U-net can be used as an efficiency tool in multi-physics analysis and achieve good performance with only small datasets.

It is shown that DL based on U-net can be used as an efficiency tool in multi-physics analysis and achieve good performance with only small datasets.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

This paper aims to present the plan to develop the known algorithm for thermal and electromagnetic coupled problem calculation. This is used for a one‐phase induction motor with locked rotor for nominal and lowered voltage excitation values. It also aims to prepare a calculating method for the average heat transfer coefficient for natural convection from the induction motor housing external face.

The numerical investigations proposed are based on 3D finite element models for thermal and electromagnetic fields analysis and 3D volume element model for average heat transfer coefficient calculations. The thermal model is experimentally validated.

The paper provides a numerical method to calculate average heat transfer coefficient for the induction motor housing external faces. This coefficient is shown as a temperature function. Temperature variations in the various parts of the induction motor with locked rotor are calculated. The calculation results are compared with the measurement results.

The average heat transfer coefficient is calculated for a limited range of temperature and for the natural convection case. Electromagnetic field analysis does not include losses in the motor core. These losses could be included in the thermal and electromagnetic fields coupled calculation problem as an additional heat source for the thermal field.

The paper presents a 3D transient thermal field and electromagnetic field coupled problem and proposes a method for calculating the average heat transfer coefficient of natural convection from the housing external face of the induction motor with a locked rotor.

The purpose of this paper is to present the plan to develop the known algorithm for thermal and electromagnetic coupled problem calculation. This is used for three‐phase induction motor (IM) on nominal load. An additional purpose is verification empiric expressions of the heat transfer and equivalent thermal conductivity coefficients for external faces and air zones in analysed motor taken from literature.

The numerical investigations proposed in this paper are based on 3D finite element models for thermal and electromagnetic fields analysis. Electromagnetic analysis includes iron core losses. It gives additional heat sources to thermal analysis. Heat transfer and equivalent thermal conductivity coefficients are assessed applying empiric expressions. Thermal model is experimentally validated.

The results of calculations and experimental test shows that heat transfer coefficient for external zones taken from literature does not guarantee the equal accuracy of the distribution of the temperature in all volume of the machine.

Taken from literature, empirical equations do not give correct values of heat transfer coefficient. It states ways to go further in the evaluation of heat transfer coefficients.

This paper presents modelling methodology of 3D transient thermal field coupled with electromagnetic field applied in three‐phase IM at rated load conditions.

The purpose of this paper is to apply a 3D methodology to assess the heating hazard on transformer covers and present a practical tool to design amagnetic inserts arrangement.

A practical 3D methodology linking an electromagnetic analytical formulation with thermal finite element method is used for computation. Such methodology allows the evaluation of the temperature on metallic device elements heated by electromagnetic induction. This is a 3D problem which in the case of power transformers becomes especially difficult to apply due to the discretization requirement into the thin skin depth penetration compared to big machine dimensions.

From the numerical solution of the temperature field, decisions on dimensions and different amagnetic inserts arrangements can be taken to avoid hot spots on transformer covers.

Some parameters presented in the model as heat exchange coefficients and material properties are difficult to determine from formulae or from the literature. The accuracy of the results strongly depends on the proper identification of those parameters, which the authors adjust based on measurements.

Differing from previous works found in the literature, which focus their results in power loss computation methods, this paper evaluates losses in terms of temperature distribution, which is easier to measure and validate over transformer covers. Moreover, an experimental work is presented where the temperature distribution is measured over a steel cover plate and a cover plate with amagnetic insert.

This paper aims to develop a new quasi-three dimensional (3D) analytical model devoted to the study of nonlinear transient magneto-thermal coupled problems in permanent magnet (PM) transverse flux induction heating device (TFIHD).

The presented work is based on analytical development of strongly coupled problem, including electromagnetic and thermal boundary problems. The electromagnetic problem is first solved by using the separation variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained thanks to strong involvement of this magnetic model in a new analytical thermal model combining the separation of variables method and the Green’s functions transient regime analysis method. The coupled model is then used in a simulation procedure of the magneto-thermal process allowing taking into account the workpiece electrothermal nonlinear properties. The developed coupled model is validated by computing the performances of the studied PM TFIHD and comparing them to those obtained by finite element simulations.

An efficient transient quasi-3D magneto-thermal analytical model is developed allowing rapid analysis of PM induction heating for core heating of parallelepiped parts. The developed model also allows fast and accurate simulations of nonlinear and transient three dimensional (3D) magneto-thermal phenomena for planar induction heaters.

The developed quasi-3D magneto-thermal analytical model is limited to design induction heating devices of planar structure with PM inductors.

A new transient quasi-3D magneto-thermal analytical model accounts for non-linearity and edge effect and helps to fast study and fast design of linear permanent magnet induction heating device.

This work aims to study a new design of linear permanent magnet transverse flux induction heating devices of nonmagnetic parallelepipedic workpiece. In these topologies, the permanent magnet inductor produces a static magnetic field, and the workpiece to be heated is subjected to a linear movement. To study the magnetothermal process, a new analytical coupling method between the magnetic and thermal phenomena is developed. This analytical model described in this study takes into account the variation of the physical properties of the heated workpiece. The analytical results are compared with good agreement to those issued from finite elements simulations, as well as those issued from measurements on an actual prototype.

The research methodology is based on analytical development of coupled problem, including the electromagnetic and thermal boundary problems. A strongly coupled magneto-thermal analytical model is developed; the time dependent magnetic problem is first solved by using the separation of variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained, thanks to strong involvement of this magnetic model in a new analytical thermal model based on a synergy of separation of variables method and Green’s function transient regime analysis method.

The results show that an efficient transient magneto-thermal analytical model was developed allowing fast analysis of permanent magnet induction heater for deep heating of parallelepipedic workpieces. Developed model allows also fast and precise simulations of nonlinear and transient magneto-thermal phenomena for different types of permanent magnet induction heating devices.

The developed magneto-thermal analytical model can be used for fast designing of permanent magnet linear induction heating devices for moving parallelepipedic nonmagnetic workpiece.

A new analytical coupled model, including the electromagnetic and transient thermal boundary problem with additional algebraic equations and taking into account the nonlinearity, has been developed. The developed model accuracy was validated with a permanent magnet linear induction heating device. Developed coupled analytical model allows fast analysis and designing of such permanent magnet linear induction heating devices.

This paper aims to deal with the 3D finite element analysis of metallic sheets heating in translating motion through the air gap of an inductor of transverse flux type.

This study presents two finite element based motion coupling techniques used to analyze the transient temperature field of moving metallic sheets heated by induction.

The numerical results obtained by the two different magneto‐thermal – translating motion coupling techniques proposed in this paper are in good agreement with each other being validated also by experimental measurements.

The proposed numerical techniques can be used for the design and optimization of transverse flux induction heating systems.

An original solution to improve the transversal thermal profile of the metallic sheet based on the magnetic shielding is proposed and analyzed. The numerical results of the thermal field are validated by experimental measurements.

This paper presents the results of a series of tests made in order to validate the magneto‐thermal module of the new FLUX3D v3.40. The tool was conceived to solve the coupled problems of electromagnetic and thermal phenomena. The solving method of the program considers a thermal‐transient problem during a certain period of time and it solves, at each time step, the thermal and electromagnetic equations (in quasi‐stationary magneto‐harmonic formulation), alternatively. We have modelled the inductive longitudinal welding of steel pipes. The results of 3D simulations are compared with measurements on a laboratory device.

In analysing coupled electromagnetic thermal behaviours in electrical devices one of the main difficulties is related to the uncertainties of thermal parameters. The authors present, in this work, a technique using the method of experimental designs for the identification of thermal parameters necessary for a coupled finite element model analysing the magneto‐thermal behaviour of an electromagnetic device.